Phase diagram and universality of the Lennard-Jones gas-liquid system

Abstract

The gas-liquid phase transition of the three-dimensional Lennard-Jones particles system is studied by molecular dynamics simulations. The gas and liquid densities in the coexisting state are determined with high accuracy. The critical point is determined by the block density analysis of the Binder parameter with the aid of the law of rectilinear diameter. From the critical behavior of the gas-liquid coexisting density, the critical exponent of the order parameter is estimated to be β = 0.3285(7). Surface tension is estimated from interface broadening behavior due to capillary waves. From the critical behavior of the surface tension, the critical exponent of the correlation length is estimated to be ν = 0.63(4). The obtained values of β and ν are consistent with those of the Ising universality class.

Ostwald ripening in multiple-bubble nuclei

“…Based on our empirical basis, the size of subcells are small enough to resolve bubble configurations and large enough to identify phases between gas and liquid [17,22]. The densities of the gas and liquid coexisting in this system at the typical temperature T = 0.9 are estimated to be 0.0402(2) and 0.6790 (9), respectively [20]. Here, we chose 0.2 as the density threshold, i.e., a subcell having less than six particles is defined to be in the gas state.…”

“…We first maintain the system in the pure-liquid phase using the Nosé-Hoover thermostat [19]. In a past study, the binodal line between the liquid and coexisting phases of this system was determined to be ρ b (T ) = aT + b + c(T c − T ) β , where a = −0.195(1), b = 0.533(1), c = 0.5347(4), T c = 1.100(5), and β = 0.3285(7) [20]. Using these parameters, we set the initial density as ρ = 1.04 × ρ b (T ), i.e., the initial density is set to 4% higher than the coexisting density ρ b at a given temperature.…”

Dynamics of homogeneous nucleation

“…= 5.0 ±2 , of the particle nearest the center of mass of the cluster, which corresponds to a density ρ ≈ 0.46, reveals that the local sphere at the center is not very liquid-like. (The densities of the corresponding liquid and gas at T = 0.80 are ρ l =0.7367 and ρ g =0.0174, respectively [24], and with a mean coordination number, n co.no. (l)=9.02 in the liquid and a potential energy per particle, u(l) = −5.116.…”

Simulation of pattern dynamics of cohesive granular particles under a plane shear

“…Note that this density corresponds to the critical density for Lennard-Jones fluid at equilibrium [24,25,26]. We fix the system size L x = L y = 52σ , L z = 12σ for this density.…”

“…The existence of the attractive force causes some new features due to the competition of the gas-liquid phase transition [24,25,26] and the dissipative structure [7]. For instance, nucleation process near equilibrium is well understood [27], but that under a shear is not well understood.…”